The title of the question says it all, basically. During the 1500s when there was trade between Europe and Japan, were European-style plate armours sold or traded to the Japanese? Are there any depictions or recorded instances of any Japanese fighting men adopting European plate?

Yes, it is often menthioned that parts of European Armour where incorporated into Japanese ones.
These would be exemples of such incorporation:
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[ Linked Image ]

Considering that the most important weapons on the Japanese battlefield were pike and musket (or at least yari and musket), it isn't surprising that bullet-resistant breastplates were probably the most popular Western addition to Japanese armours.

I've seen photos of Japanese helmets with European bowls.

In Arms and Armour of the Samurai by I. Bottomley and A.P. Hopson, there is a photo of a French Napoleonic cuirrasier armour that has been modified to suit Japanese tastes.

Supposedly (according to the book), full sets of genuine foreign armour was a rarity that only the wealthy could afford. . Usually, ony the cuirass, helmet and gorget were used. Some suits that seem to consist of a western cuirass and helmet turn out to be inspired copies

What was less rare though was the usage of Western helmets. The cabasset was popular for this. These helmets were modified to take a Japanese style neckguard. The Momonari kabuto (peach shaped helmet), was inspired by the appearance of modified European cabasset helmets. Simple Cuirasses were also imported and outfitted with tassets in the Japanese style and were often given a russet finish.

European armour in japanese use is covered in the spotlight artivle on the evolution of japanese armour; http://www.myArmoury.com/feature_jpn_armour.html